Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binary_search(arr, low, high, x):
 
    if high >= low:
 
        mid = (high + low) // 2
 
        if arr[mid] == x:
            return 1
 
        elif arr[mid] > x:
            return binary_search(arr, low, mid - 1, x)
 
        else:
            return binary_search(arr, mid + 1, high, x)
 
    else:
        return 0

import math
n = int(input())
n = n*(1+1)
t = []
flag = 1
for i in range(1,int(math.sqrt(n))+1):
    t.append(i*(i+1))
k = len(t)-1
for i in range(1,int(math.sqrt(n))+1):
    if(binary_search(t,0,k,n-i*(i+1))):
        print("YES")
        flag = 0
        break
if(flag):
    print("NO")